You want to lightly sand your cabinets first before painting them. You should use a good quality latex gloss or semi-gloss paint. Either of those would be washable. .I prefer latex because it is water wash up and better for the environment. There are some great non-toxic paints listed for kids rooms that would work good for kitchen cabinets. I would use them.
My contractor recommends Kilz especially for a kitchen. As far as paint brands, I have never been disappointed with Sherwin Williams paints. They might be a tad more expensive, but the coverage and durability is phenomenal. Their staff also makes great recommendations for remodeling. For example, I had a pernicious mold problem around my bathroom windows. They directed me to a product that can be added to paints that prevents mold. It was great.
I have used this additive extensively in my basement as well.